Estimating single-crystal elastic constants of polycrystalline β metastable titanium alloy: A Bayesian inference analysis based on high energy X-ray diffraction and micromechanical modeling

Highlights: • A Bayesian framework with high-energy X-ray diffraction and elastic self-consistent (ELSC) micromechanical model is successfully employed to identify the single-crystal elastic constants and their uncertainities in a near-β titanium alloy (Ti–10V–2Fe–3Al). • Among the different material parameters (grain texture, morphology, volume fraction) of the micromechanical model, the grains morphology was found to be significant in obtaining best fit with experimental data. • The Bayesian identified single crystal elastic constants of the β phase are $C_{11}^{\beta }=92.6\pm 19.1\mathrm{GPa},C_{12}^{\beta }=82.5\pm 16.3\mathrm{GPa},C_{44}^{\beta }=43.5\pm 7.1\mathrm{GPa}$ accounting for prolate spheroid grains with aspect ratio of ~3.8$\pm 0.8$. A two-phase near-β titanium alloy (Ti–10V–2Fe–3Al, or Ti-1023) in its as-forged state is employed to illustrate the feasibility of a Bayesian framework to identify single-crystal elastic constants (SEC). High Energy X-ray diffraction (HE-XRD) obtained at the Diamond synchrotron source are used to characterize the evolution of lattice strains for various grain orientations during in situ specimen loading in the elastic regime. On the other hand, specimen behavior and grain deformation are estimated using the elastic self-consistent (ELSC) homogenization scheme. The XRD data and micromechanical modelling are revisited with a Bayesian framework. The effect of different material parameters (crystallographic and morphological textures, phase volume fraction) of the micromechanical model and the biases introduced by the XRD data on the identification of the SEC of the β phase are systematically investigated. In this respect, all the three cubic elastic constants of the β phase ($C_{11}^{\beta },C_{12}^{\beta },C_{44}^{\beta }$) in the Ti-1023 alloy have been derived with their uncertainties. The grain aspect ratio in the ELSC model, which is often not considered in the literature, is found to be an important parameter in affecting the identified SEC. The Bayesian inference suggests a high probability for non-spherical grains (aspect ratio of $\sim 3.8\pm 0.8$) : $C_{11}^{\beta }=92.6\pm 19.1\mathrm{GPa},C_{12}^{\beta }=82.5\pm 16.3\mathrm{GPa},C_{44}^{\beta }=43.5\pm 7.1\mathrm{GPa}$. The uncertainty obtained by Bayesian approach lies in the range of ~1-3 GPa for the shear modulus ${\mu }^{\prime }=\frac{C_{11}^{\beta }-C_{12}^{\beta }}{2}$, and ~7 GPa for the shear modulus ${\mu }^{″}=C_{44}^{\beta }$, while it is significantly larger in the case of the bulk modulus $\frac{C_{11}^{\beta }+2C_{12}^{\beta }}{3}$ (~17-24 GPa).